Abstract
Analytic expressions for the two dimensional \( \mathcal{N}=1 \) SLFT blocks in the light semi-classical limit are found for both Neveu-Schwarz and Ramond sectors. The calculations are done by using the duality between SU(2) \( \mathcal{N}=2 \) super-symmetric gauge theories living on R 4 /Z 2 space and two dimensional \( \mathcal{N}=1 \) super Liouville field theory. It is shown that in the light asymptotic limit only a restricted set of Young diagrams contributes to the partition function. This enables us to sum up the instanton series explicitly and find closed expressions for the corresponding \( \mathcal{N}=1 \) SLFT four point blocks in the light asymptotic limit.
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References
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
M. Green, J. Schwarz and E. Witten, Superstring theory: volume 1. Introduction, Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge U.K. (1988).
A.M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981) 207.
A.B. Zamolodchikov, Infinite additional symmetries in two-dimensional conformal quantum field theory, Theor. Math. Phys. 65 (1985) 1205 [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].
A. Losev, N. Nekrasov and S.L. Shatashvili, Testing Seiberg-Witten solution, in the proceedings of the Strings, branes and dualities, May 26–June 14, Cargese, France (1997).
N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, Prog. Math. 244 (2006) 525 [hep-th/0306238] [INSPIRE].
R. Flume and R. Poghossian, An algorithm for the microscopic evaluation of the coefficients of the Seiberg-Witten prepotential, Int. J. Mod. Phys. A 18 (2003) 2541 [hep-th/0208176] [INSPIRE].
H. Poghosyan, R. Poghossian and G. Sarkissian, The light asymptotic limit of conformal blocks in Toda field theory, JHEP 05 (2016) 087 [arXiv:1602.04829] [INSPIRE].
A.M. Polyakov, Quantum geometry of fermionic strings, Phys. Lett. B 103 (1981) 211.
A.B. Zamolodchikov and R.G. Poghossian, Operator algebra in two-dimensional superconformal field theory (in Russian), Sov. J. Nucl. Phys. 47 (1988) 929 [INSPIRE].
D. Friedan, Z.-a. Qiu and S.H. Shenker, Superconformal invariance in two-dimensions and the tricritical Ising model, Phys. Lett. 151B (1985) 37 [INSPIRE].
M.A. Bershadsky, V.G. Knizhnik and M.G. Teitelman, Superconformal symmetry in two-dimensions, Phys. Lett. 151B (1985) 31 [INSPIRE].
H. Eichenherr, Minimal operator algebras in superconformal quantum field theory, Phys. Lett. 151B (1985) 26 [INSPIRE].
A. Belavin and B. Mukhametzhanov, N = 1 superconformal blocks with Ramond fields from AGT correspondence, JHEP 01 (2013) 178 [arXiv:1210.7454] [INSPIRE].
A. Belavin, V. Belavin and M. Bershtein, Instantons and 2d superconformal field theory, JHEP 09 (2011) 117 [arXiv:1106.4001] [INSPIRE].
V. Belavin and B. Feigin, Super Liouville conformal blocks from N = 2 SU(2) quiver gauge theories, JHEP 07 (2011) 079 [arXiv:1105.5800] [INSPIRE].
F. Fucito, J.F. Morales and R. Poghossian, Multi instanton calculus on ALE spaces, Nucl. Phys. B 703 (2004) 518 [hep-th/0406243] [INSPIRE].
F. Fucito, J.F. Morales and R. Poghossian, Instanton on toric singularities and black hole countings, JHEP 12 (2006) 073 [hep-th/0610154] [INSPIRE].
V.A. Belavin, N = 1 supersymmetric conformal block recursion relations, Theor. Math. Phys. 152 (2007) 1275 [hep-th/0611295] [INSPIRE].
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ArXiv ePrint: 1706.07474
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Poghosyan, H. The light asymptotic limit of conformal blocks in \( \mathcal{N}=1 \) super Liouville field theory. J. High Energ. Phys. 2017, 62 (2017). https://doi.org/10.1007/JHEP09(2017)062
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DOI: https://doi.org/10.1007/JHEP09(2017)062